Curriculum and Textbook Content
Debate continues over the effectiveness of two distinct instructional approaches: (1) emphasis on drill and practice activities in which students work toward skill mastery and (2) emphasis on reasoning, conceptual understanding, and skill application. This debate is driven by differences in opinion regarding the nature of the curriculum as well as different theories about how people learn. Although whole-group instruction and worksheets are still commonly used , the majority of American teachers report using small-group instruction as well as using manipulatives or models to demonstrate a concept (Henke, Chen, and Goldman 1999.) Data from the TIMSS video study indicate, however, that teacher implementation of the kinds of instructional techniques for mathematics advocated in the NCTM standards are often superficial. National data that link these approaches to differences in learning outcomes are sparse. This section reviews the most recent data available on curriculum and instruction.
Data from the TIMSS video study show considerable cross-national variation in curricular approaches used in mathematics instruction. For example, American and German middle school mathematics lessons focus primarily on the acquisition and application of skills, but Japanese lessons stress problem solving and thinking. Furthermore, the quality of U.S. mathematics lesson plans was judged to be substantially below that in Germany and Japan in an evaluation by U.S. college mathematics teachers. International studies have also shown that U.S. math and science textbooks cover comparatively more topics with less depth of coverage and development. Recent studies by the American Association for the Advancement of Science (AAAS) have found the most widely used middle school mathematics textbooks and high school science (e.g., biology) textbooks to be less than satisfactory (AAAS 1999a, b and 2000a, b.)
Both the new mathematics and the new science standards envision instruction that challenges students, but neither provides an exact blueprint for action. Measuring the extent to which this vision is becoming a reality is difficult because available methods cannot measure quality directly. Instead, educational researchers have relied most often on indicators of the amount of time students spend studying a subject (classwork and homework), the content of lessons, and the types of instructional resources used (e.g., textbooks). This section reviews instructional and curricular topics where recent data collection and research have been strongest: international comparisons of time spent studying mathematics and science, cross-national comparisons of curricular structure, and evaluations of the quality of mathematics and science textbooks. Although these lines of research have yielded valuable information for education policymakers, much remains to be learned about how to make mathematics and science instruction more effective.
The question of whether U.S. students spend enough time in school or receiving instruction has persisted for many years, and research results on this issue are mixed. Research by Stigler and Stevenson (1991) showed that U.S. students spend fewer hours in school than Japanese students and that U.S. schools allocate less time to core instruction than do other industrialized nations. For example, core academic time in U.S. schools was estimated at 1,460 hours during the four years of high school compared with 3,170 hours in Japan. NECTL reported in 1994 that at the time of the Commissions study, only 10 states specified the number of hours to be spent in academic subjects at various grades. Only eight others provided recommendations regarding academic time. Based on these and other findings, the Commission concluded: "[T]ime is the missing element in the debate about the need for higher academic standards.
We have been asking the impossible of our studentsthat they learn as much as their foreign peers while spending only half as much time in core academic studies" (NECTL 1994.)
This may not be the case for mathematics and science, as 1995 and 1999 data for 8th graders from TIMSS and TIMSS-R suggest. Eighth-grade students in the United States receive at least as much classroom time in mathematics and science instruction as students in other nations: close to 140 hours per year in mathematics and 140 hours per year in science in 1994-95. (See figure 1-13 .) Students in Germany, Japan, and the United States spent about the same amount of time on a typical homework assignment, but U.S. students were assigned homework more often, thus increasing total time spent studying in the two subjects (Beaton et al. 1996b; NCES 1997a, c and 1996c.)
Certain caveats are necessary in interpreting results on instructional time. First, in other nations, particularly Japan, students participate in extracurricular mathematics and science activities in afterschool clubs or in formal tutoring activities. Second, disruptions for announcements, special events, and discipline problems in U.S. classrooms considerably reduce the amount of classroom time actually spent on instructional activities (Stigler et al. 1999.)
Curriculum and Textbook Content
Analyses conducted in conjunction with TIMSS (Schmidt, McKnight, and Raizen 1997) documented that curriculum guides in the United States include more topics than is the international norm. Most other countries focus on a limited number of topics, and each topic is generally completed before a new one is introduced. In contrast, U.S. curriculums follow a "spiral" approach: topics are introduced in an elemental form in the early grades, then elaborated and extended in subsequent grades. One result of this is that U.S. curriculums are quite repetitive, because the same topic appears and reappears at several different grades. (See figure 1-14 .) Another result is that topics are not presented in any great depth, giving the U.S. curriculum the appearance of being unfocused and shallow.
The Schmidt, McKnight, and Raizen (1997) study also suggests that U.S. curriculums, especially math, make fewer intellectual demands on students, delaying until later grades topics that are covered much earlier in other countries. U.S. mathematics curriculums also were judged to be less advanced, less challenging, and out of step with curriculums in other countries. The middle school curriculum in most TIMSS countries, for example, covers topics in algebra, geometry, physics, and chemistry. Meanwhile, the grade 8 curriculum in U.S. schools is closer to what is taught in grade 7 in other countries and includes a fair amount of arithmetic. Science curriculums, however, are closer to international norms in content and in the sequence of topics. Textbooks reflect the same inadequacies documented by curriculum analyses: insufficient coverage of many topics and insufficient development of topics. (See figure 1-14 .) Compared to textbooks used in other countries, science and mathematics textbooks in the United States convey less challenging expectations, are repetitive, and provide little new information in most grades, a finding reported in earlier research by Flanders (1987) and by Eyelon and Linn (1988.) Publishers have made some attempts to reflect the topics and demands conveyed by the educational standards; however, the TIMSS curriculum analyses suggest that when new "standards-referenced" topics are added, much of the old material is retained (Schmidt, McKnight, and Raizen 1997.)
Recent studies by AAAS (1999a, b) have reinforced the findings of TIMSS and other studies about the inadequacies of mathematics and science textbooks. AAAS conducted a conceptual analysis of content based on 24 instructional criteria and applied them to the evaluation of 9 middle-school science texts and 13 mathematics texts. The samples included the most widely used texts in both subjects. Each text was evaluated by two independent teams of middle school teachers, curriculum specialists, and science and mathematics education professors. AAAS developed and tested the evaluation procedure over a three-year period in collaboration with more than 100 scientists, mathematicians, educators, and curriculum developers. On a 0- to 3-point scale (where 3 represents "satisfactory"), all nine science textbooks scored below 1.5. Six mathematics texts scored below 1.5, and only three scored above 2.5 points (AAAS 1999a, b.)
Similar evaluations of high school biology and algebra texts were only slightly more supportive of their content. In a 2000 evaluation of 10 widely used and newly developed biology textbooks, none received high ratings (AAAS 2000b.) Two independent teams of biology teachers, science curriculum specialists, and professors of science education evaluated each biology text, along with its teacher guide. The evaluation examined how well the texts are likely to help students learn the important ideas and skills in the widely accepted Benchmarks for Science Literacy (developed earlier by AAAS Project 2061) and in the National Science Education Standards (NRC 1996.) Directors of this study reported, for example, that the textbooks ignore or obscure the most important biological concepts by focusing instead on technical terms and trivial details (which are easy to test) and that activities and questions included are inadequate to help students understand many of the more difficult concepts.
Among the 12 high school algebra textbooks evaluated by AAAS Project 2061, 7 were considered adequate; however, not one was rated highly (AAAS 2000a.) Five textbooks, including three that are widely used in American classrooms, were rated so inadequate that they lack potential for student learning. Highlights of the evaluation included the following:
- All of the textbooks present algebra using a variety of contexts and give students appropriate firsthand experiences with the concepts and skills.
- Most of the textbooks do an acceptable job of developing student ideas about algebra by representing ideas, demonstrating content, and providing appropriate practice.
- No textbook does a satisfactory job of providing assessments to help teachers make instructional decisions based specifically on what their students have or have not learned.
- No textbook does a satisfactory job of building on students existing ideas about algebra or helping them overcome their misconceptions or missing prerequisite knowledge.
Most information about instructional practice has come from surveys that asked teachers about specific aspects of their teaching. In a recent survey, 82 percent of full-time U.S. mathematics teachers and 74 percent of full-time science teachers gave themselves good grades on using practices consistent with educational standards in their fields (NCES 1999d.) However, classroom observational studies, which have provided more depth and dimension to depictions of practice, often paint quite a different picture. These studies demonstrate that it is relatively easy for teachers to adopt the surface characteristics of standards-based teaching but much harder to implement the core features in everyday classroom practice (Spillane and Zeuli 1999; Stigler et al. 1999; and NCES 2000d.)
The TIMSS video study of 8th-grade mathematics instruction is a case in point. Lessons in U.S., German, and Japanese classrooms were fully documented, including descriptions of the teachers actions, students actions, amount of time spent on each activity, content presented, and intellectual level of the tasks that students were given in the lesson (Stigler et al. 1999.) These findings identified four key points:
- The content of U.S. mathematics classes requires less high-level thought than classes in Germany and Japan.
- The typical goal of U.S. mathematics teachers is to teach students how to do something, but the typical goal of Japanese teachers is to help them understand mathematical concepts.
- Japanese classes share many features called for by U.S. mathematics reforms, but U.S. classes are less likely to exhibit these features.
- Although most U.S. mathematics teachers report familiarity with reform recommendations, relatively few apply the key points in their classrooms.
Ratings by mathematicians of the quality of instruction in 8th-grade German, Japanese, and U.S. mathematics classrooms in 199495 suggest a lower level of quality in U.S. instruction. Approximately 30 percent of lessons in Japanese classrooms were rated as "high quality" and 13 percent were rated as "low quality." In German classrooms, 23 percent of lessons received high ratings and 40 percent received low ratings. In comparison, approximately 87 percent of U.S. lessons were considered "low quality" and none were considered "high quality." (See figure 1-14 .) However, because of the small scale of the study, these results are suggestive rather than definitive. The studies are now being replicated on a larger scale in both mathematics and science.